The reality is that wealth and happiness are often not compatible either. As for "poverty" - how do you define poverty? If you knew my circumstances I'm sure you would class me as being very poor indeed - however I am more content and happy than most of the people I know. I don't have children, but if I did there are many qualities I would try to instil ahead of being money driven, which probably wouldn't even make the list at all. I find it rather sad that there are still people who believe the pursuit of money always leads to happiness.
I don't think anyone is arguing that you can't be poor and happy (same as they aren't arguing that you can't be rich and unhappy), but that it is easier to be happy if you have money because you've removed the worry of not being able to afford basics.
I'm definitely happier now I'm on a slightly higher income, just knowing that (unless something goes horribly wrong) I can afford food and bills every month makes a huge difference. I will say that being poor was slightly easier to cope with when I didn't have kids, it was less stressful when I only had to worry about affording food/bills for myself.